Active Contour Technique Based On Minimum Description Length Principle

Image segmentation, one of the fundamental techniques of image processing, has been widely used in various fields, such as medical image processing, remote sensing, and the related aspects. Of all kinds of image segmentation techniques, the active contour segmentation technique owns the best feature as far as segmentation accuracy concerned. In fact, this technique is attracting much attention of research and application. The existing active contour techniques, however, still suffer from a few or more defects, such as the high sensitivity to noise, the tight limitation on the initial contour position and the image contents, and the lack of topological adaptability, which impose a heavy restriction on the application of these techniques.In order to develop a practicable active contour technique usable in the real world, we should carefully analyze and sufficiently make use of the properties of the image as a random field; we should have a methodology to translate the underlying principle for image segmentation, such as the homogeneity of properties of the image on the object region, into a mathematically amenable model; and also we need a methodology to control the regularity of the produced contour while it closely approaches the boundary of the object in the image. Unfortunately, none of the existing active contour techniques can fully meet these requirements. With the help of the Minimum Description Length (MDL) principle, we regard these requirements as the corresponding description lengths. On this basis, we deduce the energy functional for image segmentation. Thus, we have a new kind of active contour technique-MDL active contour technique. The basic idea of MDL is to set up a math model that can accurately describe the object while make description length shortest. As a result, the MDL principle can attain higher model accuracy while the model complexity is lowest. Experiments shows that the proposed MDL active contour technique can wipe out the mentioned defects of the existing active contour techniques.The innovation of the work of this paper can be listed as follows: 1. Based on the MDL principle, a new energy functional is proposed. This functional can describe properties of the image as a random field, the regionhomogeneity properties and the regularity properties of active contour. For the image with random field feature, the description language is probability distribution model, and the description length equals the negative base-two logarithm of the probability of the image data; For the region homogeneity properties of active contour, the description language is chosen as a sign gradient map, and the description length is the summation of sign gradient inside the active contour; For the active contour regularity, the description language is smoothness, and the corresponding description length is the length of active contour curve. The proposed energy functional can make use of advantages of the region information and the edge information. The region number, region feature parameters and edge position can be estimated simultaneously when this functional is minimized.2. Based on the proposed energy functional, we proposed a new parametric active contour technique-The Parametric B-Spline MDL Active Contour. This technique is composed of two steps. Firstly, given the seed point of the interesting region, it detects the edge points that has the shortest distance to seed point in some directions, takes these points as the control points to form the initial B-Spline active contour. Secondly, it minimizes the above energy functional by Lagrangian algorithm to obtain the accurate edge. In order to make this technique be with the topological adaptability, we propose an efficient topological technique, which is based on the change of region Euler number. Experiments show the efficiency of our Parametric B-Spline MDL Active Contour.3. Based on the proposed energy functional, we proposed a new geometric active contour technique-The Geometric MDL Active Contour. Firstly, this technique smo...